Question: Is one supposed to cover a bare arm before reciting tachanun (nefilas apayim)? E.g., if a person is wearing a short-sleeved shirt (or t-shirt) is it acceptable to recite tachanun in this attire?
Introduction: Historically, nefilas apayim was performed literally, and people would “fall on their faces” i.e., bow down fully on the ground (as we do nowadays during Mussaf on Rosh Hashanna and Yom Kippur).
The minhag of nefilas apayim in contemporary times is not to “fall on one’s face” literally, but to bend one’s head and cover one’s face (Mishna Berura Siman 131 s.k. 3).
Answer: The Mishna Berura (ibid) writes that the minhag when reciting tachanun is to cover one’s face with a garment, and it is not sufficient to cover one’s face with one’s hand.
Therefore, one should try to somehow cover one’s arm (with a jacket, coat or even tallis) when reciting tachanun, and not just cover one’s face with one’s hand.